Radiation and it properties

if we place a very thin rod of length 'l' in front of a source of some radiation of amplitude = length of the rod (l) ,and perpendicular to its direction of propagation (assuming all the radiation to be polarized in one particular direction), :-

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(rod of length 'l') (radiation falling on the rod perpendicular to its length)

DOUBT 1: Won't it cause the electrons in the rod to oscillate across its full length (perhaps for some particular wavelength/frequency) generating alternating current in the rod?

DOUBT 2: Also, if it does, what would be the relation between the frequency of the current generated in the rod to the frequency of the involved radiation?

This would appear to be a question about radio antennae (not exclusively but the following applies directly to antennae).

An alternating current is induced in a wire by a passing em wave. There is little point discussing the effect on the actual electrons in the wire because the movement that's induced is sub-atomic in magnitude for RF frequencies. Just stick to talking about current; we're talking in terms of a very classical phenomenon.
The frequency of that current is the same as the exciting radiation - it has to be, what else could it be? The amplitude of the current will depend on the length of the conductor and will be maximum when the length is resonant at the frequency of the em wave.

I used the word "passing" because this even applies to an infinitely thin conductor, which would have zero physical cross sectional area to intercept the wave. Nonetheless, it does intercept the wave and behaves as it it has an effective width (or cross section) in the order of the wavelength involved.

This would appear to be a question about radio antennae (not exclusively but the following applies directly to antennae).

An alternating current is induced in a wire by a passing em wave. There is little point discussing the effect on the actual electrons in the wire because the movement that's induced is sub-atomic in magnitude for RF frequencies. Just stick to talking about current; we're talking in terms of a very classical phenomenon.
The frequency of that current is the same as the exciting radiation - it has to be, what else could it be? The amplitude of the current will depend on the length of the conductor and will be maximum when the length is resonant at the frequency of the em wave.

I used the word "passing" because this even applies to an infinitely thin conductor, which would have zero physical cross sectional area to intercept the wave. Nonetheless, it does intercept the wave and behaves as it it has an effective width (or cross section) in the order of the wavelength involved.

So if we have a very large array of such tiny* and thin** rods ,and some apparently perpetual source of radiation (like a star -- our sun), such that a huge amount of appropriately polarized*** radiation is made to fall on all the rods, won't this generate power perpetually in principle (as long as the source exists)?

if so, what are the practical limitations/constraints to implementing such a method?

*(the length of all the rods being predetermined by the wavelength of the available radiation, such that resonance is possible)

**(hopefully the word 'thin' could be used almost properly while assuming the thickness of the rod to be very small compared to the wavelength of the radiation involved?)

***(electric field linearly polarized in the plane containing the rod and the line formed by the direction of propagation)

The RF energy received off any one antenna ( pretty much regardless of the frequency you use) is a VERY SMALL amount. The multiple antenna system would have to be quite huge to even just light a 12V 5W lightbulb

As part of my radio astronomy experiments over the years, I have listened to the sun on various frequencies. The Voltage levels are measured in microVolts

if so, what are the practical limitations/constraints to implementing such a method?

There is loads of energy reaching the Earth from the Sun - about 1kW/sq metre at the equator - enough to keep us warm and for all the plants to grow for us that we could need - if we could only manage it properly.
You seem to be suggesting that we are somehow missing a trick by not using RF technology to make use of the majority of the radiation that reaches Earth, which is visible light. There are better ways, namely photosynthesis (the majority mechanism, with good reason) and Photovoltaic cells, which work on the QM level. There are also many other, indirect ways of using the energy from the Sun, involving Wind, Tide and Wave energy conversion.

For 'RF' style methods to be used, you don't only need the right length antenna but you also need some equivalent to the 'circuitry' associated with antennae. That's a bit difficult as you're talking about molecular dimensions (600nm ish, which is at the peak of the received spectrum from the Sun) That could prompt you to use the word "nanotechnology". Well, I can't dismiss it out of hand but you would need to propose something concrete rather than just say the word. to convince me.

The RF energy received off any one antenna ( pretty much regardless of the frequency you use) is a VERY SMALL amount. The multiple antenna system would have to be quite huge to even just light a 12V 5W lightbulb

As part of my radio astronomy experiments over the years, I have listened to the sun on various frequencies. The Voltage levels are measured in microVolts

having trouble in determining the resonance condition for the rod of length (l) at driving frequency (f) = 500*10^12 Hz......
please explain how to do that?

Look up 'resonant dipoles'.
You can do the sums but the wavelength(s) of light is a few hundred nm. You don't get bits of wire that long and nor can you attach wires to them. To use that technology (i.e. radio antennae) you need to be tuned to wavelengths which fall on a low energy part of the Sun's spectrum (there's not much available energy in the first place. Secondly, as you need resonance for good energy transfer, you need loads of antennae to cover the wavelength range. Why do you think it's done a different way for the visible part of the spectrum?

Look up 'resonant dipoles'.
You can do the sums but the wavelength(s) of light is a few hundred nm. You don't get bits of wire that long and nor can you attach wires to them. To use that technology (i.e. radio antennae) you need to be tuned to wavelengths which fall on a low energy part of the Sun's spectrum (there's not much available energy in the first place. Secondly, as you need resonance for good energy transfer, you need loads of antennae to cover the wavelength range. Why do you think it's done a different way for the visible part of the spectrum?

the wavelength of light at peak intensity reaching the earth ~ 500 * 10^(-9) m
the power per unit area incident on the earth due to sunlight ~ 1400 W , giving the avg magnitude of electric field = the avg magnitude of magnetic field ~ √[(4π*10^-7)*1400] = .04 V/m

how to relate the length of the rod to the wavelength of the radiation?
I cannot understand why it shouldn't be JUST equal to the amplitude of the fields constituting the radiation? I know i am wrong somewhere..
please help...

the wavelength of light at peak intensity reaching the earth ~ 500 * 10^(-9) m
the power per unit area incident on the earth due to sunlight ~ 1400 W , giving the avg magnitude of electric field = the avg magnitude of magnetic field ~ √[(4π*10^-7)*1400] = .04 V/m

how to relate the length of the rod to the wavelength of the radiation?
I cannot understand why it shouldn't be JUST equal to the amplitude of the fields constituting the radiation? I know i am wrong somewhere..
please help...

The length of the dipole is related to the Wavelength and NOT the amplitude? This is because an EM wave sets up a standing wave on any length of wire and when the length is suitable for resonance (e.g. a half wavelength), the energy transferred is high. Did you look up " radio antenna, dipoles etc. "? There are good explanations all over the place. Try wiki first.

If the dipole dimensions depended upon the Amplitude of the wave, you would need different lengths of antenna at different distances from the transmitter because the amplitude drops off with distance!